Analog computer



June 22, 1965 Filed Jan. 13, 1959 FIGI FIG. 2.

FIG3.

w. D. HOLAK ETAL 3,191,016

ANALOG COMPUTER 2 Sheets-Sheet 1 INVENTORS CLIFFORD E. MCCARTY ERKKI K.HYYPOLAINEN ATTYS.

WILLIAM D. HOLAK June 22, 1965 Filed Jan. 13, 19 59 FIGS w. D. HOLAKETAL ANALOG COMPUTER 2 Sheets-Sheet 2 INVENTORSZ United States Patent3,191,016 ANALOG COMPUTER William D. Holak, Crum Lynne, Clitiord E.McQa'rty,

Ridiey Park, and Erlrki K. Hyypolainen, Chester, Pa,

assignors to Scott Paper Company, Chester, Pa, a corporation ofPennsylvania Filed Jan. 13, 1%), Ser. No. 786,564 14 Claims. (Cl.235-185) This invention relates to a simple analog computer for solvingproblems having to do with the change, exchange or flow in a mannerwhich is most efficient and/ or least costly and particularly withreference to determining maximum flow under given sets of conditions.

Generally speaking, and with the exception of certain internallimitations, the computer is capable of solution of problems of thisgeneral sort by selection of power as the analog of the quantity to beminimized, and selection of other parameters according to their relativenatures, if the problem can be set up as linear simultaneous equationswithin specified limits.

In its most general form, the analog computer of the present inventionconsists of a network having three types of terminals which representinput, output and intermediate terminals and which provide networknodes. The internal network is defined as that part of the networkbetween the input and output terminals and consists of flow pathsconnecting together various terminals including intermediate terminals.All of the terminals are not necessarily connected to one another buteach terminal is connected into the network in such a way as to provide,by means of its various flow paths, a continuous flow route betweeninput and output terminals. Each flow path has a potential producingelement arranged to oppose the general direction of fiow. Ordinarily,but not necessarily, each flow path will also have a flow rectifyingmeans to insure unidirectional flow in that path. The individual flowpaths are preferably to this extent similar to those described in thecopending applications of William C. Elmore and Clifford E. McCarty, nowUS. Patent No. 2,934,273, and Clifford E. McCarty and William D. Holak,now U.S. Patent No. 3,017,104. Additionally the flow paths may havemeans for limiting the total amount of flow to represent a specifiedload capacity. External of the internal network at least one conductiveconnection between output and the input terminals and including a flowgenerator, is provided.

The present invention diiiers from the two abovespecified inventionsbecause of the provision for internal terminals or nodes. The provisionof these internal terminals permits complex internal networks notpossible in the computers considered in the aforesaid applications. Theterminals or nodes in the contemplation of the present invention may bemore than a junction point. They may be energy-consuming points, energyproducing points, flow-limiting points, or combinations thereof, in anyof which cases the node is no longer a simple node in a usual sense buta split node effectively having an input terminal and an output terminalwith the energy-consuming element and/or energy producing element and/or flowlirniting element and/ or potential producing element in the flowpath between the terminals. Such terminals or nodes enable the solutionof problems of greater complexity and details than the twoabove-mentioned computers .which are designed to handle more generalproblems. The present computer may find wide application in analysis ofdetailed information in order to obtain more general information for usein other computers, such as the two above mentioned.

The present invention also introduces the concept of the split nodewhereby not only the flow paths between tints Patented June 22, 1965nodes have some effect upon the current but the nodes themselves mayhave an effect upon the current. The split node is nothing more than anode which is divided so that it effectively has an internal tic-w pathfrom one part of the node to the other in which various'types offlow-resisting elements, limiting elements and/ or potential producingelements may be introduced. In this arrangement the current flows to onepart of the split node and away from the other part of the split node.At the present time it is contemplated that a maximum capacity flowlimiter may be used in this location or a resistive element may be usedbetween the divided parts of the split node but other applications maycall for additional elements such as a potential producing elementbetween the parts of the split node.

The flow-limiting device may have a variety of forms, one of which willbe specifically described herein. The flow-limiting device will findwider application than strictly in a computer having internal networknodes and there is no intention to limit it to the specific form ofcomputer described herein although it is useful with such a com puter.

The computer of the present invention will find wide use as a generaltransportation computer. It is useful,

' for example, to determine the manner in which freight should be routedin order to permit it to reach its destination most efficiently andprobably leastexpensively. In the usual problem, the nodes may benumbered from 1 to N, and the flow paths described in terms of the nodeswhich they link, the how path linking nodes i and 1' being designated byL This general type of problem might be described as the networkutilization problem which can be stated as follows:

Where X,,- denotes the rate of flow of product through link L find a setof flowsrthrough the links which maximize the total flow in the node N.

The problem may be subject to certain restraints. F or example, X inmany cases must be positive and must not exceed a certain maximum loadcapacity.

Many possibilities exist with the computer of the present invention. Abetter understanding of the present invention may be had by reference tothe following drawings in which:

.FIG. 1 shows a network having internal terminals arranged in parallelflow routes;

FIG. 2 illustrates a computer having plural internal terminals arrangedin series in a single flow route;

PEG. 3 shows a computer in accordance with the present invention havinga composite arrangement;

FIG. 4 schematically shows a computer of the present invention includingcross link flow paths, the fiow paths of which have flow-limiting means;

FIG. 5 is a computer according to the present invention similar to FiG.4 but having separate flow paths for travel in both directions betweencertain terminals;

FIG. 6 is a detailed showing of one form of flow-limiting device inaccordance with the present invention;

FIG. 7a shows one form of split node;

FIG. 7b shows another form of split node; and

FIG. shows still another form of split node.

Referring first to FIG. 1, there is shown a computer network having aninput terminal 10, an output terminal 11 and two intermediate terminals12 and 13. The network between input and output terminals 19 and 11including the intermediate terminals 12 and 13 represents the internalnetwork. Each of the flow paths 14 connecting terminals 19 and 12, 12and 11, 16 and 13, and 13 and 11 includes potential-producing means 15.Means insuring the flow only in opposition to the potential-producingmeans need not be used in this arrangement since there is no alternativeprovided that the current fiow externally generated is not reversed. Asshown, there is connected to the input terminal 16 a constant flowgenerator 16, which in turn is connected in series within an externalflow path 17 connecting terminals 11 and 19 together. In the circuit ofFIG. 1, current divides at terminal .10 and flows partially through node12 and partially through node 13 to terminal 11.

Referring to FIG.'2, an arrangement is shown in which there is an inputterminal 20, an output terminal 21 and two intermediate terminals 22 and23. In this case, the terminals 22 and 23 are connected in series withone another and the input andoutput terminals by series flow paths 24 toprovide a single continuous flow route from terminal to terminal 21comprising the internal network. Each of the flow paths 24 havepotential-producing means 25 and may contain flow-rectifying means aswell, although such rectifying means are unnecessary because of thesimplicity of this particular network and in view of the fact that flowgenerator 26 at output node 21 produces flow in a proper direction atall times. An external connection 27 completes the circuit betweenoutput terminal 21, flow generator 26 and input terminal 20.

Referring now to FIG. 3, there is shown schematically a computer whichhas an internal network which is a composite of the networks of internalnetworks of FIGS. 1 and 2. Between an input terminal 30 and an outputterminal31 are intermediate terminals 32, 33 and 34. Terminals 32 and 33are connected in series with'the terminals 30 and 31 by theirintermediate flow paths 35 to provide a continuous flow route. Aparallel continuous flow route is provided through terminal 34 fromterminal 30 to terminal 31 through similar intermediate flow paths 35.Each of the flow paths in this instance has a potential-producing means36 plus means for producing a unidirectional fiow 37. Flow is induced byaconstant fiow generator 38 at the input terminal 30 and constant flowgenerator 39 at the output terminal. These generators are in turnconnected together by external connection 40. If preferred, therectifier means 37 may be omitted in this particular form.

Referring next to FIG. 4, a much more complex array is illustrated. Thenodes which in the general problem are numbered from 1 to 10 are herenumbered 1, 2, 3, 4 and 5, and N where 1 is the basic input terminal andN is the basic output terminal. Terminal 2 may also be considered aninput terminal, and terminal 4 may also be considered an outputterminal, although .by another viewpoint they may be considered specialeffect nodes in accordance with the needs of a particular problem.

In FIG. 4flow generator 41 produces a flow into node 1, and flowgenerator 42 produces a flow out of node N. Flowgenerator 43 producesflow into node 2, and flow generator 44 produces a flow out of node 4.Nodes 1 and 2 are connected together by flow path 45. Nodes 2 and 4 areconnected by flow path 46. Nodes 4- and N areconnected by flow path 47.Flow paths 45, 46 and 47, and nodes 1, 2, 4 and N thereby provide aseries ilow route. Similarly, nodes 1, 3, 5 and N are linked by flowpaths 43, 49 and 50 in a series flow route. The two paths thus describedare parallel flow paths'which might be thought of as alternate routesalong which trucks may move through various cities represented by nodes.Interconnecting routes from 2 to 3 or from 4 to 5 are provided by flowpaths 51 and 52. Additionally, other flow paths 53 and 54 interconnectnodes 2 and 5 and 3 and 4, respectively. Under certain circumstances itmay be desirable for detours to be'taken.

FIG. 5 shows a similar arrangement to FIG. 4 wherein similar parts areindicated by similar numbers having the same designator with theaddition of primes thereto. FIG. 5. provides, however, for travel ineither direction between intermediate nodes, or at least some of them.Thus, 'in addition to flow from terminal 2' to terminal 3' along route51', there can be a flow from terminal 3'. to terminal 2 along flow path55. Between terminals 4' 4;, and 5 flow proceeds in one direction overflow path 52' and in the other direction over flow path 56. Alternateflow paths between terminals 2' and 5', 3' and 4' are provided by flowpaths 57 and 58. Additionally, alternate flow paths are provided betweenterminals 2 and 4', 3' and 5 by flow paths 59 and 60.

Within the flow paths, as illustrated, are potential producing devices61 arranged to oppose the flow of cur.- rent which is limited to flow inone direction through the flow path by rectifying means 62.Additionally, flow capacity limiting devices 63' are provided and may beset at dilferent levels to restrict a particular capacity in accordancewith the analog of the problem undergoing solution. 7

' Referring to FIG. 6, there is shown schematically one arrangement fora flow limiting device of an electrical type. In this arrangement anormally closed relay switch 65 normally shorts out a flow limitingresistor 66 intended to limit current flow through the series circuitbranch which is placed in series in the flow path. The relay 67 isarranged to open the switch 65 upon the attainment of a certain currentlevel through to the device. This may be determined by resistor 68 inseries with the switch 65, the voltage across which is amplified byamplifying means 69 and fed to a comparison means 70 such that, whenthe, voltage corresponding to the capacity of the device is reached, therelay 67 is actuated opening the switch 65 and there opposing theresistance 66 to limit current flow. Preferably, the flow limitingdevice is a multi-step switching arrangement not as simple as describedabove but one (not shown) which includes a plurality of switches 65,relays 67 and comparison means 76 appropriately arranged to provide amaximum cur-v rent restriction for the flow path.

Many other types of current limiting arrangements are available, and theone shown in FIG. 6 is by way of illustration rather than by way oflimitation.

The present invention also contemplates the splitting of internal nodes.For example, in a particular instance a node like node 4 of'FIG. 4 mightbe split to introduce a resistor element '73 between the parts of thenode 4a and 4b, as shown in FIG. 7a. At another point, for example, node5 whichmight be split into node portions 5a and 5b, a current limitingelement (such as that shown in FIG. 6) might be introduced as element 71in series between the terminals 5a and 5b as shown in FIG. 7b. In FIG.70 there is shown a split node consisting of parts 3a and 3b, betweenwhich is placed a potential producing element 72. Combinations of suchelements (not shown) may be introduced in such split nodes.

Considering a network like that of FIG. 5, by eliminating differentportions of the network, it can be visualized how problems of differentform can be set up on a computer. For example, eliminate flow generators43' and 44 and any external circuit which they may include so that nodes2' and 4 are clearly internal nodes and a typical single supply, singledemand situation is achieved. The potential producing means may be setto represent cost, the time to travel a particular flow path link, orwhatever other limiting factor applies. As shown in FIG. 4, at most, onelink joins any two nodes, node 1 is a source of some product and node Nis the only demand point for this product. In order to simplify, it canbe assumed that the product can be shipped homogen-i ously in a sensethat it can flow in a continuous fashion through links rather than onlyin discrete truck loads or train loads. With each link or flow path Lthere is associated a non-negative load capacity limiting element. Thisload capacity is to be interpreted as the maximum sustained rate ofone-way flow which the link is capable of bearing for one reason oranother and dimensionally.

may be described in terms of tons per day, for example.

The limitations of the general network utilization problem describedabove apply and if X denotes the rate of flow of the product throughflow path L then it is possible,

to find a set of flows through the various links which maximize thetotal flow in node N subject to the following restraints or limitations:(1) X must be non-negative and must not exceed C (determined by the loadcapacity limiting means) and (2) the total flow into any intermediatenode, i.e., nodes 2, 3, to N1, must equal the total flow out of thatnode. The last restraint is to the efiect that none of the product isconsumed or absorbed except at N and it follows that the effect of theproblem is to maximize the total flow out of node 1.

The problem stated can be changed by conditions within the nodes whichrepresent cities oifering general bottlenecks to the flow of traflic,for example. Thus, by use of the split node technique described above,it is possible to put a load capacity limitation or a handling ortransfer cost at a node whereby regardless of the capacities of theindividual flow paths or links leading into the node, the node imposes aseparate limitation upon the flow.

Whenever a flow generator, such as 43 or 44 is introduced at a node, anew limitation is imposed in place of the second limitation abovestated. Thus, for example, the total flow into the node 2 must exceedthe total flow out of the node, considering only flow paths, by theamount of flow added to the node by flow generator 43. The converse ofthis is true if the flow is out of the node, as at node 4.

The physical interpretation of the arrangement of the flow generators atthe nodes 2 and 4 may be that these nodes are points of limited constantproduction or consumption of the product. The objective remains that ofmaximizing flow to N. This need not be the case, however, and both flowgenerators 41 and 43 may supply nodes 1 and 2, respectively, as inputnodes which are sources of the product and flow generators 42 and 44 maybe connected to output terminals 4 and N so that they both may representpoints of demands. In such case, the problem becomes one of maximizingthe flow from all sources of supply to all demand points. Somecircumstances may require the introduction of artificial nodes whichhave no physical significance in order to set up a problem of this typebut no limitation is placed upon the physical significance or lackthereof of the nodes and flow paths or other portions of the computer.

The computer has been described for the most part in generalterminology, even though the networks illustrated have been D.C.electrical systems. In such systems, the constant flow devices areconstant flow generators, the flow paths are conductors, and the nodesare junction points of several conductors, except in the special case ofsplit nodes, where they are two junction points separated by aconductive path including some element; The potential-producing means inthis case is a battery, and the rectifying means is preferably a dioderectifier.

In other embodiments, the computer of the present invention may appearas an AC. network, a mechanical network or as a fluid network eitheremploying hydraulic or pneumatic components. All modifications withinthe scope of the claims are intended to be within the spirit of theinvention.

We claim:

1. In an analog computer, a network having a plurality of terminalsincluding at least one input terminal, one output terminals, one ofwhich flows routes includes said stituting network nodes in an internalnetwork, said internal network having at least two flow routes eachcomprising at least one flow path connecting said input and outputterminals, one of which flow routes includes said intermediate terminaldividing such flow route into two flow paths, at least one potentialsource element in at east one of the flow paths in the internal networkand rectifiers in enough of the flow paths to eliminate circulating flowin the internal network, and at least one flow path including a constantflow generator between the output and input terminals external of theinternal network, the improvement comprising at least one element in atleast one of said routes of the internal network to limit flow throughsaid route to a predetermined maximum which element consumes essentiallyno energy in the process until a predetermined current level isexceeded.

2. The analog computer of claim 1 in which there are intermediateterminals connected in series as well as intermediate terminals inparallel flow paths.

3. The analog computer of claim 2 in which terminals in parallel flowpaths are connected together by cross flow paths.

4. The analog computer of claim 1 in which there is a constant flowgenerator at the input and output terminal of the network.

5. The analog computer of claim 1 in which there are a plurality ofinput terminals each having a constant flow generator associated with itand each input terminal having a continuous flow route to an outputterminal.

6. The analog computer of claim 1 in which there are a plurality ofoutput terminals each having an associated constant flow generator, andeach input terminal having a continuous flow route through the fiowpaths to an output terminal.

7. The analog computer of claim 1 in which some of the terminals havetwo paths between them, each limiting flow to the opposite directionfrom the other.

8. The analog computer of claim 1 in which there are at least twointermediate terminals serially disposed in a single flow route dividingsuch flow route into three flow paths.

9. The analog computer of claim 1 in which there are at least twointermediate terminals each in a diiferent flow route.

10. The analog computer of claim 8 in which atleast some of theintermediate terminals have two paths between them, each limiting flowto the opposite direction from the other.

11. The analog computer of claim 1 in which at least one of theterminals is a split node wherein the node is split into two separatedterminal points between which is introduced an electrical element havingsome analog significance corresponding to a condition occurring at theanalog of a nodal point.

12. The analog computer of claim 11 in which between the split nodalportions there is introduced a resistor element.

13. The analog computer of claim 11 in which between the split nodalportions there is introduced a flow limiting element.

14. The analog computer of claim 11 in which between the split nodalportions there is introduced a potential producing element.

References Cited by the Examiner UNITED STATES PATENTS 2,569,646 10/51Wade et al. 235180 XR 2,608,770 9/52 Hansford 235--184 XR 2,639,089 5/53Gleyzal 235-180 2,639,357 5/53 Kesselring 323--96 2,884,193 4/59Liebmann 235184 2,934,273 4/60 Elmore et al. 235185 2,960,646 11/60Malsbury 323- 3,053,453 9/62 Bock et al. 235l MALCOLM A. MORRISON,Primary Examiner. LEO SMILOW, WALTER W. BURNS, 111., Examiners.

UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No,3,191,016 June 22, 1965 William D. Holak et a1 It is hereby certifiedthat error appears in the above numbered patent requiring correction andthat the said Letters Patent should read as corrected below Column 5,lines 64 and 65, strike out "output terminals, one of which flows routesincludes said stituting network nodes in an internal network, said in"and insert instead output terminal, and one intermediate terminalconstituting network nodes in an internal network, said in- Signed andsealed this 21st day of December 1965.

(SEAL) Attest:

ERNEST W. SWIDER EDWARD J. BRENNER Attesting Officer Commissioner ofPatents

1. IN AN ANALOG COMPUTER, A NETWORK HAVING A PLURALITY OF TERMINALSINCLUDING AT LEAST ONE INPUT TERMINAL, ONE OUTPUT TERMINALS, ONE OFWHICH FLOWS ROUTES INCLUDES SAID STITUTING NETWORK NODES IN AN INTERNALNETWORK, SAID INTERNAL NETWORK HAVING AT LEAST TWO FLOW ROUTES EACHCOMPRISING AT LEAST ONE FLOW PATH CONNECTING SAID INPUT AND OUTPUTTERMINALS, ONE OF WHICH FLOW ROUTES INCLUDES SAID INTERMEDIATE TERMINALDIVIDING SUCH FLOW ROUTE INTO TWO FLOW PATHS, AT LEAST ONE POTENTIALSOURCE ELEMENT IN AT LEAST ONE OF THE FLOW PATHS IN THE INTERNAL NETWORKAND RECTIFIERS IN ENOUGH OF THE FLOW PATHS TO ELIMINATE CIRCULATING FLOWIN THE INTERNAL NETWORK, AND AT LEAST ONE FLOW PATH INCLUDING A CONSTANTFLOW GENERATOR BETWEEN THE OUTPUT AND INPUT TERMINALS EXTERNAL OF THEINTERNAL NETWORK, THE IMPROVEMENT COMPRISING AT LEAST ONE ELEMENT IN ATLEAST ONE OF SAID ROUTES OF THE INTERNAL NETWORK TO LIMIT FLOW THROUGHSAID ROUTE TO A PREDETERMINED MAXIMUM WHICH ELEMENT CONSUMES ESSENTIALLYNO ENERGY IN THE PROCESS UNTIL A PREDETERMINED CURRENT LEVEL ISEXCEEDED.